The Cai δ-equality of fuzzy sets corresponds to the Lukasiewicz t-norm. In this paper we study the notion of (∗, δ)-equality, a concept which generalizes the δ-equality to the case of the fuzzy set theory based on an arbitrary continuous t-norm ∗. We investigate the robustness of some fuzzy implication operators in terms of (∗, δ)-equality.

In this paper, we introduce a special algebra called EQ-algebra which has three binary operations (meet, product, fuzzy equality) and a top element. The fuzzy equality is reflexive, symmetric and transitive with respect to the product. EQ-algebra is a natural algebra proposed as an algebra of truth values on the basis of which the fuzzy type theory (a higher-order fuzzy logic) should be develop...

ÐWe propose a new measure of fuzzy equality comparison based on the similarity of possibility distributions. we define a type of fuzzy equi±join based on the new fuzzy equality comparison, and allow threshold values to be associated with predicates of the join condition. A sort±merge join algorithm based on a partial order of intervals is used to evaluate the fuzzy equi-join. In order for the e...

Fuzzy relations on the same domain are classified according to the equality of families of cut sets. This equality of fuzzy relations is completely characterized, not only for unit interval valued fuzzy relations, but more generally, for fuzzy relations whose domain is a (complete) lattice. Similar results for fuzzy sets in general are considered in [12]. Applications of the results for fuzzy c...

Abstract An E -fuzzy group is a lattice-valued algebraic structure, defined on a crisp algebra which is not necessarily a group. The crisp equality is replaced by a particular fuzzy one denoted by E . Classical group-like properties are formulated as appropriate fuzzy identities special lattice theoretic formulas. We prove basic features of E -fuzzy groups: properties of the unit and inverses, ...

Possibilistic linear equality systems (PLES) are linear equality systems with fuzzy parameters and crisp variables. We study the problem: For a given PLES with weakly noninteractive fuzzy number parameters how does the solution change if the parameters are varied?

In this paper two new concepts are introduced: the similarity and the (∗,δ)-equality of fuzzy choice functions. We investigate the manner the similarity and (∗,δ)-equality behave with respect to some fundamental concepts of fuzzy revealed preference theory. Keywords– Fuzzy choice function, Revealed preference, Similarity relation.

We argue that fuzzy equivalences, and in particular fuzzy equalities, in general are not suitable to model approximate equality due to the notion of transitivity. Using them for this purpose therefore leads to counter-intuitive results, as we illustrate in detail in a fuzzy relationbased framework for the representation of linguistic modifiers. We solve the problem by choosing resemblance relat...

Park et al. (2011) introduced the concept of generalized intuitionistic fuzzy soft sets, which can be seen as an effective mathematical tool to deal with uncertainties. In this paper, the concept of generalized intuitionistic fuzzy soft equality is introduced and some related properties are derived. It is proved that generalized intuitionistic fuzzy soft equality is congruence relation with res...

In this paper, we introduce a new algebra called ‘EQ-algebra’, which is an alternative algebra of truth values for formal fuzzy logics. It is specified by replacing implication as the main operation with a fuzzy equality. Namely, EQ-algebra is a semilattice endowed with a binary operation of fuzzy equality and a binary operation of multiplication. Implication is derived from the fuzzy equality ...